ON BEHAVIOR OF TRAJECTORIES OF WEAK SOLUTIONS OF N-DIMENSIONAL STOCHASTIC NAVIER-STOKES EQUATIONS
The research paper study a behavior of trajectories of weak solutions of n-dimensional (n≥2) Navier-Stokes equations, perturbed by an additive white noise. It is shown that at any given moment t trajectories in its subsequent motion along the phase space of the system: a) inevitably leave any bounde...
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| Format: | Article |
| Language: | Russian |
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MIREA - Russian Technological University
2017-06-01
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| Series: | Российский технологический журнал |
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| Online Access: | https://www.rtj-mirea.ru/jour/article/view/70 |
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| author | D. A. Khrychev |
| author_facet | D. A. Khrychev |
| author_sort | D. A. Khrychev |
| collection | DOAJ |
| description | The research paper study a behavior of trajectories of weak solutions of n-dimensional (n≥2) Navier-Stokes equations, perturbed by an additive white noise. It is shown that at any given moment t trajectories in its subsequent motion along the phase space of the system: a) inevitably leave any bounded subset of the phase space; b) inevitably return to some compact set K, depending on the viscosity and on the external forces acting on the system. Thus, it is established that the trajectories alternately go away arbitrarily far from the mentioned set K, then again return to it, i.e. the recurrence of trajectories in relation to the set K and infinity. These results are obtained by estimating the mathematical expectation of the moments of the first exit of trajectory after t from the corresponding subsets of the phase space. |
| format | Article |
| id | doaj-art-bcee688d761c40429c6b35f6be1908dc |
| institution | Kabale University |
| issn | 2782-3210 2500-316X |
| language | Russian |
| publishDate | 2017-06-01 |
| publisher | MIREA - Russian Technological University |
| record_format | Article |
| series | Российский технологический журнал |
| spelling | doaj-art-bcee688d761c40429c6b35f6be1908dc2025-08-20T03:40:03ZrusMIREA - Russian Technological UniversityРоссийский технологический журнал2782-32102500-316X2017-06-015315115910.32362/2500-316X-2017-5-3-151-15970ON BEHAVIOR OF TRAJECTORIES OF WEAK SOLUTIONS OF N-DIMENSIONAL STOCHASTIC NAVIER-STOKES EQUATIONSD. A. Khrychev0Moscow Technological University (MIREA)The research paper study a behavior of trajectories of weak solutions of n-dimensional (n≥2) Navier-Stokes equations, perturbed by an additive white noise. It is shown that at any given moment t trajectories in its subsequent motion along the phase space of the system: a) inevitably leave any bounded subset of the phase space; b) inevitably return to some compact set K, depending on the viscosity and on the external forces acting on the system. Thus, it is established that the trajectories alternately go away arbitrarily far from the mentioned set K, then again return to it, i.e. the recurrence of trajectories in relation to the set K and infinity. These results are obtained by estimating the mathematical expectation of the moments of the first exit of trajectory after t from the corresponding subsets of the phase space.https://www.rtj-mirea.ru/jour/article/view/70stochastic navier-stokes equationsweak solutionssolution trajectories |
| spellingShingle | D. A. Khrychev ON BEHAVIOR OF TRAJECTORIES OF WEAK SOLUTIONS OF N-DIMENSIONAL STOCHASTIC NAVIER-STOKES EQUATIONS Российский технологический журнал stochastic navier-stokes equations weak solutions solution trajectories |
| title | ON BEHAVIOR OF TRAJECTORIES OF WEAK SOLUTIONS OF N-DIMENSIONAL STOCHASTIC NAVIER-STOKES EQUATIONS |
| title_full | ON BEHAVIOR OF TRAJECTORIES OF WEAK SOLUTIONS OF N-DIMENSIONAL STOCHASTIC NAVIER-STOKES EQUATIONS |
| title_fullStr | ON BEHAVIOR OF TRAJECTORIES OF WEAK SOLUTIONS OF N-DIMENSIONAL STOCHASTIC NAVIER-STOKES EQUATIONS |
| title_full_unstemmed | ON BEHAVIOR OF TRAJECTORIES OF WEAK SOLUTIONS OF N-DIMENSIONAL STOCHASTIC NAVIER-STOKES EQUATIONS |
| title_short | ON BEHAVIOR OF TRAJECTORIES OF WEAK SOLUTIONS OF N-DIMENSIONAL STOCHASTIC NAVIER-STOKES EQUATIONS |
| title_sort | on behavior of trajectories of weak solutions of n dimensional stochastic navier stokes equations |
| topic | stochastic navier-stokes equations weak solutions solution trajectories |
| url | https://www.rtj-mirea.ru/jour/article/view/70 |
| work_keys_str_mv | AT dakhrychev onbehavioroftrajectoriesofweaksolutionsofndimensionalstochasticnavierstokesequations |